Hexagonal boron nitride (h-BN) lattice structure is a kind of hexagonal symmetric complex superlattice structure. In recent years, photonic crystals with h-BN superlattice structure have attracted growing attentions due to their unique properties of wide photonic band gaps. A new h-BN superlattice plasma photonic crystal (SPPC) constructed by periodically arranging gas discharge tubes and Al2O3 dielectric rods is proposed in this paper. The positions, widths and numbers of band gaps for h-BN superlattice and triangular lattice plasma photonic crystal (PPC) have been compared. The effects of the discharge current, numbers of dielectric rod rows and incident angles of electromagnetic waves in different frequencies have been demonstrated. The results show that the introduction of plasma enables tunable structural configurations and plasma parameters for h-BN SPPC. It not only produces new photonic band gaps, but also selectively shifts the band gap positions. Compared with the simple triangular PPC, h-BN SPPC possesses more photonic band gaps. Moreover, the numbers of dielectric rod rows have significant influences on the positions, widths and numbers of band gaps. The correlation of transmission spectra decrease with the increase of incident angle of electromagnetic waves. The novel h-BN SPPC suggested in this work provides some inspiration for creating new types of tunable metamaterials, which has potential applications in the manipulation of microwave and terahertz waves.